scholarly journals Effective Flow of Micropolar Fluid through a Thin or Long Pipe

2011 ◽  
Vol 2011 ◽  
pp. 1-18 ◽  
Author(s):  
Igor Pažanin
Keyword(s):  
Cross Section ◽  
Asymptotic Approximation ◽  
Micropolar Fluid ◽  
Variable Cross Section ◽  
Asymptotic Model ◽  
Variable Cross ◽  
Straight Pipe ◽  
Micropolar Fluid Flow ◽  
Flow Through ◽  
Explicit Formulae

The aim of this paper is to present the result about asymptotic approximation of the micropolar fluid flow through a thin (or long) straight pipe with variable cross section. We assume that the flow is governed by the prescribed pressure drop between pipe's ends. Such model has relevance to some important industrial and engineering applications. The asymptotic behavior of the flow is investigated via rigorous asymptotic analysis with respect to the small parameter, being the ratio between pipe's thickness and its length. In the case of circular pipe, we obtain the explicit formulae for the approximation showing explicitly the effects of microstructure on the flow. We prove the corresponding error estimate justifying the obtained asymptotic model.

scholarly journals Asymptotic Approximation of the Nonsteady Micropolar Fluid Flow through a Circular Pipe

2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Igor Pažanin ◽  
Marko Radulović
Keyword(s):  
Asymptotic Approximation ◽  
Micropolar Fluid ◽  
Fluid Velocity ◽  
Nonsteady Flow ◽  
Cylindrical Pipe ◽  
Numerical Examples ◽  
Micropolar Fluid Flow ◽  
Flow Through ◽  
Explicit Formulae ◽  
Velocity Approximation

We study the nonsteady flow of a micropolar fluid through a thin cylindrical pipe. The asymptotic behaviour of the flow is found via asymptotic analysis with respect to the small parameter ϵ, representing the pipe’s thickness. The asymptotic approximation is derived in the form of the explicit formulae for the fluid velocity and microrotation. We also provide the numerical examples in order to visualize the effects of the micropolar nature of the fluid. The illustrations indicate the influence of the micropolarity on the effective flow of the fluid in the whole domain. In particular, those effects are most clearly observed for the velocity approximation near the boundary of the domain.

scholarly journals Compressible flow through solar chimneys with variable cross section - an exact solution

2017 ◽  
Vol 44 (2) ◽  
pp. 215-228
Author(s):  
Vladan Djordjevic ◽  
Aleksandar Cocic
Keyword(s):  
Compressible Flow ◽  
Cross Section ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Mathematical Methods ◽  
Power Series Expansions ◽  
Number Flow ◽  
Flow Through ◽  
Low Mach Number Flow

Buoyancy driven, adiabatic and compressible flow in relatively high solar chimneys is treated in the paper analytically by using one-dimensional model of flow. General equations written suitably in a non-dimensional form are used for a qualitative discussion pertaining to the mutual effects of gravity, viscosity and varying cross section of the chimney. It is shown that in case of low Mach number flow these equations possess exact solutions obtainable by ordinary mathematical methods for any given chimney shape. Also shown, and demonstrated on an example, is the procedure of evaluation of the chimney shape that satisfies a condition imposed beforehand upon the flow. For better insight into the role of various parameters the solutions are presented in the form of power series expansions.

Mathematical Model Of Liquid Flow Through The Pipe Of Curcular Cross-Section

2016 ◽  
Vol 11 (4) ◽  
pp. 61-67
Author(s):  
Eduard Arinstein ◽  
Denis Tokarev
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Liquid Flow ◽  
Analytical Approach ◽  
Variable Cross Section ◽  
Cylindrical Symmetry ◽  
Variable Cross ◽  
Current Line ◽  
Flow Velocity Profile ◽  
Flow Through

This article analyses the properties of homogeneous viscous liquid flow in the pipe with variable cross-section characterized by cylindrical symmetry. The analytical approach is proposed in order to determine the flow velocity profile in the pipe’s extremium cross-sections. The conditions when dead spaces emerge in neighborhood of the maximum cross-section are identified. The particular case of problem-solving allowing prime presentation is examined for the set of current line allowing prime presentation.

Pressure Losses in Power-Law Fluid Flow through a Tube of Variable Cross-Section

2021 ◽  
Vol 56 (1) ◽  
pp. 1-9
Author(s):  
E. I. Borzenko ◽  
I. A. Ryl’tsev ◽  
G. R. Schrager
Keyword(s):  
Fluid Flow ◽  
Cross Section ◽  
Power Law ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Power Law Fluid ◽  
Pressure Losses ◽  
Flow Through
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